A Nonlinear Conditional Gaussian Framework for Extreme Events Prediction, State Estimation, and Uncertainty Quantification in Complex Dynamical System

A nonlinear conditional Gaussian framework for extreme events prediction, data assimilation and uncertainty quantification in complex dynamical systems will be introduced in this talk. In the first part of this talk, the general framework of the nonlinear conditional Gaussian systems, including a gallery of examples in geophysics, fluids, engineering, neuroscience and material science, will be presented. In the second part, an efficient statistically accurate algorithm is developed for solving the Fokker-Planck equation in large dimensions, which is an extremely important and challenging topic in prediction, data assimilation and uncertainty quantification. This new efficient algorithm involves a novel hybrid strategy for different subspaces, a judicious block decomposition and statistical symmetry. Rigorous mathematical analysis shows that this method is able to overcome the curse of dimensionality. In the third part, a low-order model within the nonlinear conditional Gaussian framework is developed to predict the intermittent large-scale monsoon extreme events in nature. The nonlinear low-order model shows higher prediction skill than the operational models and it also succeeds in quantifying the uncertainty in prediction